Problem: $C$ $J$ $T$ If: $ CT = 83$, $ CJ = 2x + 9$, and $ JT = 7x + 2$, Find $JT$.
From the diagram, we can see that the total length of ${CT}$ is the sum of ${CJ}$ and ${JT}$ $ {CJ} + {JT} = {CT}$ Substitute in the expressions that were given for each length: $ {2x + 9} + {7x + 2} = {83}$ Combine like terms: $ 9x + 11 = {83}$ Subtract $11$ from both sides: $ 9x = 72$ Divide both sides by $9$ to find $x$ $ x = 8$ Substitute $8$ for $x$ in the expression that was given for $JT$ $ JT = 7({8}) + 2$ Simplify: $ {JT = 56 + 2}$ Simplify to find ${JT}$ : $ {JT = 58}$